Help with frequency response of guitar tone circuit

[dimensionless]

The circuit of interest is the basic circuit for a Fender Stratocaster guitar. A diagram can be found at http://www.seymourduncan.com/support/schematics/S_1singlecoil_1vol_1tone.html . Basically an electric guitar works by vibrating a metal string in a magnetic field. This in turn causes a current to be generated in the an inductor that is wrapped around the magnet.

What I'm trying to do is find the frequency response of this circuit. Whenever I try to calculate the transfer function for this circuit I get

$$TF = 1$$.

When I try to calculate the total impedance for this circuit I get

$$Z_{total} = \frac{Z_{1}Z_{2}}{Z_{1}+Z_{2}} = \frac{(R_{1} - j\frac{1}{\omega C})R_{2}}{R_{1}-j \frac{1}{\omega C}+R_{2}}$$

where
$$Z_{1} = R_{1} - j \omega C$$ and $$Z_{2} = R_{2}$$.

To find the transfer function I calculate

$$TF = \frac{V_{in}}{V_{out}} = 1$$.

This is obviously incorrect, but I don't know where my mistake is. Is my diagram correct?

 

[dimensionless]

My post is a litle confusing. I had an ACII diagram, but it did not get rendered the way I wnated it to. R2 is the volume pot, and R1 is the tone pot.

 

[ravenprp]

First of all, it's great that you are trying to understand the frequency response of the guitar tone circuit for your Fender Stratocaster. This is an important aspect of understanding the overall sound and tone of your guitar.

Looking at the diagram, it seems like your calculations are correct. The transfer function for this circuit is indeed 1, which means that the output voltage will be the same as the input voltage. This is because there are no capacitors or inductors in the circuit that would cause a phase shift or attenuation of the signal.

However, the frequency response of this circuit is not solely determined by the transfer function. It also depends on the values of the resistors and capacitors in the circuit. In this case, the values of R1, R2, and C are fixed, so the frequency response will be determined by those values.

To fully understand the frequency response of this circuit, you can plot the impedance as a function of frequency. This will give you a better idea of how the circuit responds to different frequencies. You can also experiment with different values of R1, R2, and C to see how it affects the frequency response.

Overall, your diagram seems correct and your calculations are accurate. The key to understanding the frequency response of this circuit is to consider the values of the components and how they affect the impedance at different frequencies. I hope this helps and happy tinkering with your guitar tone!